A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. including part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
In order to monitor the lithographic process, it is necessary to measure parameters of the patterned substrate, for example the overlay error between successive layers formed in or on it. There are various techniques for making measurements of the microscopic structures formed in lithographic processes, including the use of scanning electron microscopes and various specialized tools. One form of specialized inspection tool is a scatterometer in which a beam of radiation is directed onto a target on the surface of the substrate and properties of the scattered or reflected beam are measured. By comparing the properties of the beam before and after it has been reflected or scattered by the substrate, the properties of the substrate can be determined. This can be done, for example, by comparing the reflected beam with data stored in a library of known measurements associated with known substrate properties. Two main types of scatterometer are known. Spectroscopic scatterometers direct a broadband radiation beam onto the substrate and measure the spectrum (intensity as a function of wavelength) of the radiation scattered into a particular narrow angular range. Angularly resolved scatterometers use a monochromatic radiation beam and measure the intensity of the scattered radiation as a function of angle.
The output of the scatterometer may be used to monitor the operation of a lithographic apparatus online. This is done by monitoring the values of one or more parameters of the target and adjusting the lithographic apparatus parameters accordingly in order to take any necessary corrective actions. However in order to determine the parameters of the substrate, the best match must be found between a theoretical spectrum produced from a model of the substrate and the measured spectrum produced by the reflected beam as a function of either wavelength (spectroscopic scatterometers) or angle (angularly resolved scatterometers). In either case it is necessary to have sufficient data points (wavelengths and/or angles) in the calculated spectrum in order to enable an accurate match, typically between 80 to 800 data points or more be necessary for each spectrum. In practice this leads to a compromise between accuracy and speed of processing.
In our co-pending application EP 1927893, incorporated herein by reference in its entirety, there is disclosed a method of monitoring the pupil plane, that is the back focal plane of a scatterometer, in order to detect process excursions. In the method disclosed, a fault indicator is used to notify a user by an alarm if the scatterometer image indicates any changes in the lithographic process.
In known scatterometers it is known to mathematically to model the pupil image using a rigorous coupled wave analysis (RCWA) algorithm, which is based on Maxwell's equations. Basically the parameters that describe a structure on the target, such as thickness, indices of refraction, etc., are inferred by minimizing the difference between the measured pupil plane image and the predicted pupil plane image. However, this method is very calculation intensive as the models are non-linear. Thus there is no guarantee of convergence or a unique solution being obtained. The method involves approximations being made, such as constraining some of the parameters to values that may not even be physically possible.